Problem: Michael is 24 years younger than Daniel. Daniel and Michael first met 3 years ago. Twenty years ago, Daniel was 4 times as old as Michael. How old is Daniel now?
Solution: We can use the given information to write down two equations that describe the ages of Daniel and Michael. Let Daniel's current age be $d$ and Michael's current age be $m$ The information in the first sentence can be expressed in the following equation: $d = m + 24$ Twenty years ago, Daniel was $d - 20$ years old, and Michael was $m - 20$ years old. The information in the second sentence can be expressed in the following equation: $d - 20 = 4(m - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to solve our first equation for $m$ and substitute it into our second equation. Solving our first equation for $m$ , we get: $m = d - 24$ . Substituting this into our second equation, we get the equation: $d - 20 = 4($ $(d - 24)$ $ -$ $ 20)$ which combines the information about $d$ from both of our original equations. Simplifying the right side of this equation, we get: $d - 20 = 4d - 176$ Solving for $d$ , we get: $3 d = 156$ $d = 52$.